Frugal Video Poker and Wolf Video Poker both have a function that can't be found on any other software. It's called "Tweak the Strategy Chart." I can move a hand in the strategy chart above any other hand, then analyze to get the statistics on that strategy move.

With Triple Double Bonus the optimal strategy when holding a hand like AAA3J is to hold the three Aces with the small kicker. This is reflected in the strategy chart as you will see that three Aces with the small kicker plays over three Aces. It's the same thing for the small quads, with 3332J the three 3's with the small kicker plays over holding just the three 3's. ?

With optimal strategy TDB has a payback of 99.58%.
The frequency of making Four Aces with a kicker is 14, 205.7
The frequency of making Four Aces is 6745.4.
The frequency of making Four 2's, 3's, 4's with a kicker is 5796
The frequency of making Four 2's, 3's, 4's is 3125.9

But what happens to the stats if we always hold the Three of a Kind's over the 3K's with the kicker? By tweaking the strategy chart I can get the stats. This is what happens when you never hold the kicker.

The game has an overall payback of 98.8%, about 8 tenths less than optimal strategy.
The frequency of making Four Aces with a Kicker is 16, 183.4.
The frequency of making Four Aces is 5775.
The frequency of making Small Quads with a kicker is 6815.2
The frequency of making Small Quads is 2534.

Comparing the statistics you can see that you improve your chances of making Four Aces or Small Quads, but you reduce your chances of making any of those hands with a kicker.